since i had multi conversations with the author seen in this blog, Ive decided I'll accept his nomination for the named technique and develop it further

a barn is built on the idea that a subset can be "bent" to fit out side of single box/Row/Col restrictions but instead resided inside shared sectors via shared digits so that the shared digits "lock" some of the candidates into specific cells in a way so that peers of these cells can not hold said candidates.

this thread hopes to amalgamate several low level techniques with some higher lvl functions to correlate eliminations seen but often unaccounted without resorting to a higher function logic to cover the deduction.

I discovered this concept but lacked the terms to express the deduction and concept easily way back in my wxyz-thread

when searching for a set of N candidates found In N Cells build a relation ship between the N cells by aligning them to sectors and forming a restricting link reducing the placement arrangement of N-1 candidates into n-1 cell. all peer cells of a non restricted common candidates that sees each candidate in N cells can be excluded.if all candidates are restricted to N cells then all peer cells that see each of said candidate may be excluded.

working Concept: N Cells holding N candidates: Search for a group of N Cells that are all peers of a starting point each holding up to N candidates search for sector A & Sector B where A & B contain all N cells where A <> B, and B <> AA <> empty and B <> empty

type 1: R = N-1 candidatesZ = A Candidate not found in Rboth sectors A&B contain cells for digit "z" elimination: { almost locked} all peer cells that see each "Z" candidate in sectors A&B may be excluded.

Type 3: elimination R= N -2 {almost almost locked } theorized Z = missing digits from R all peer cells for "z" that also see a situation that can place multiple or restrict multiple digit locations with in the subset may be eliminated.

Eventual further work and Goal: i would like to make this project also apply to more then just direct peer cells from a starting point as this makes barns strictly limited to 1-9 cell "wings" that in habit box+Row/col configurations, and to cover some of the examples listed below.

Allow me to understand BarnS with few (stupid) questions/suggestions as follows:

1. Is it necessary to include 3 cells/digits for BarnS?Suggest to start BarnS concept from >= 4 cells/digits combinations as XY- & XYZ-Wings do not have more types/ways to consider (as 2 c/d already not considered).

Hi StrmCkr,I'm interested in your BarnS technique, but haven't yet studied the algorithms for the two types listed. In the meantime, I'm curious to know if you have any example subsets of the N-digit/N-cell variety that cannot be solved with the Subset-Counting technique. Here, I use the term 'digit' as a 'candidate.'

I ask this question because, as I understand the older method, one need only visually examine the grid for any digit external to the subset that can 'see' all occurrences of the digit within the subset. If that happens to a multiplicity-2 digit, as it does in your samples, it would reduce the total 'multiplicity' of the subset to a value below the cell count. That would then be a contradiction and would require the external digit to be removed.

The term, multiplicity, refers to the maximum number of placements of a particular digit within a subset. Total multiplicity is the sum of all multiplicities within the subset. The digit of interest in each example above has a multiplicity of two. All others have a multiplicity of one.

SteveC

Last edited by Sudtyro2 on Thu Dec 29, 2016 10:31 pm, edited 1 time in total.

thanks for the interest Steve, i highly doubt this will bring anything new to the table elimination wise: its more of a different approach for "bending" subsets around R/C/B but not limited to the B + R/C restraints as seen in "wings"

Fits by cell count & digit count definition for a wxyz but didn't fit into the formation clause of B+R/C or R/C + C/R of a typical wing.

the sectors A&B used have no als-xz elimination and the elimination is only derived via Als-xy rules using a third sector

it doesn't fit into DDS by description as 1 is locked to R1, 3 is locked to b3 and 2,4 are not covered it would fall into Almost Almost DDS strategy found in the same link above. {where unlocked digits eliminate from all shared peers )

side note: BARN idea currently coded include these cases but currently performs no eliminations :

as a search for a set of 4 digits on 4 cells can find subset's where M candidate is missing from all found cells.

I have studied WXYZ-wings (i.e., 4-cell with exactly 4 values only) like strategy that covers within Barn. I have concluded two main types, i.e., one with pivot cell contains all four values and other with pivot cell contains only three values along with three pincer cells contain exactly four values as follows:

1) WXYZ-Wing strategy is based on four unsolved cells (abcd) align within a chute that contain exactly four values (wxyz);2) One pivot cell (a) contains all four values (wxyz) and three pincer cells (bcd) // contain exactly four values - need not to be check at this moment;3) First pincer cell (b) align with pivot cell's (a) box (or line) and other two pincers cell (cd) align with pivot cell's (a) line (or box) but not first pincer cell's (b) line;4) First pincer cell (b) contains only two values (wz) and other two pincers cell (c | d) contain exactly three values (xyz);5) First pincer cell and other two pincers cell (b & (c | d)) contain exactly one common value (z);6) First pincer cell and other two pincers cell (b & (c | d)) common value (z) may be eliminated from cells align with pivot cell (a) box and other two pincers cell (cd) (or first pincer cell (b)) common line.

1) WXYZ-Wing strategy is based on four unsolved cells (abcd) align within a chute that contain exactly four values (wxyz);2) One pivot cell (a) contain only three values (wxy) and three pincers cell (bcd) // contain exactly four values (wxyz) - may not be check at this moment;3) First pincer cell (b) align with pivot cell's (a) box (or line) and other two pincers cell (cd) align with pivot cell's (a) line (or box) but not first pincer cell's (b) line;4) First pincer cell (b) contains only two values (wz) and other two pincers cell (c | d) contain exactly three values (xyz);5) First pincer cell and other two pincers cell (b & (c | d)) contain exactly one common value (z);6) First pincer cell and other two pincers cell (b & (c | d)) common value (z) may be eliminated from cells that see those pincers cell that contain common value (z).

Note: these exemplars are not fully covered the Barn strategy but may be covered fixed patterns of WXYZ-Wings that will be easily identified/detected by either human being or computer program.

All members are welcome to share their ideas/proposals with StrmCkr here in order to discover and finalize all patterns combinations of Barn.

Yes, but this not only sounds complicated, it is by far the most complicated way i am aware to describe it.[Edit:] Now i see, that i did not post it right. What i had in mind, was in 4 boxes, not in 2:

Since the pattern here is in the same columns, the deduction is the same, as AIC:(ab=c)r34c4-(c=b)r34c1-(b=a)r3c4 => not a elsewhere in c4[oops:]correctedThis is not covered by the XYZ-Wing Hybrid, as far as i can see.

In continuation of my above mentioned post, I had stopped further studying due to the topic still not fully covered the matter. However, now I have decided to start coding for the types that I have already covered in my above mentioned post.

As I have already categorized only 40 exemplars based on pivot cell's number of digits and define three pincers as follows:

Pincers:-- First pincer shares pivot box;- Second pincer shares pivot line but not pivot box and first pincer line; and- Third pincer shares pivot either box but not second pincer line; or pivot line but not pivot box.

WXYZ-Wings Type 1:- (20 exemplars)Pivot cell contains all four digits and number of elimination cells are two.

WXYZ-Wings Type 2a:- (14 exemplars)Pivot cell contains three digits and number of elimination cells are five (instead of two).

WXYZ-Wings Type 2b:- (6 exemplars)Pivot cell contains three digits and number of elimination cells are two.

At the moment I have completed the logic, coded as entirely separate module accordingly and under rigorous testing various scenarios. Will share the source code once satisfied the performance.

That's alright the idea I have coded and shared covers, From pivot point connecting to 2-8 "wings" cells with in a box+row or box +col intersection.

For n size set of digit with in the n cells, that code works pretty good atm.

Still haven't figured out how to get it to expand into row +row or row+col, col+col types with out massive code errors.

Atm I'm working on my Als xz code as it also features the same hiccup as this codeIe overlapping sets creates errors if I have them activated once I solve that part I'll continue the barn thread. And attempt to get it to cover the project concepts.